Singular rationally connected surfaces with non-zero pluri-forms

Abstract

This paper is concerned with projective rationally connected surfaces $X$ with canonical singularities and having non-zero pluri-forms, i.e. $({\Omega }_X^1{)}^{[\otimes m]}$ has non-zero global sections for some m > 0, where $({\Omega }_X^1{)}^{[\otimes m]}$ is the reflexive hull of $({\Omega }_X^1{)}^{\otimes m}$. We show that any such surface can be obtained from a rational ruled surface by a very explicit sequence of blow-ups and blow-downs. Moreover, we interpret the existence of non-zero pluri-forms in terms of semistable reduction.

12 pages

References in corpus (2)

• Differential Forms on Log Canonical Spaces
• On codimension 1 del Pezzo foliations on varieties with mild singularities

Cited by in corpus (2)

• Singular rationally connected threefolds with non-zero pluri-forms
• Lagrangian fibrations on symplectic fourfolds